SRC/zgetrf2.f(3)

NAME
SRC/zgetrf2.f

SYNOPSIS

  Functions/Subroutines
recursive subroutine zgetrf2 (m, n, a, lda, ipiv, info)
ZGETRF2

Function/Subroutine Documentation

  recursive subroutine zgetrf2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

ZGETRF2

Purpose:

    !>
    !> ZGETRF2 computes an LU factorization of a general M-by-N matrix A
    !> using partial pivoting with row interchanges.
    !>
    !> The factorization has the form
    !>    A = P * L * U
    !> where P is a permutation matrix, L is lower triangular with unit
    !> diagonal elements (lower trapezoidal if m > n), and U is upper
    !> triangular (upper trapezoidal if m < n).
    !>
    !> This is the recursive version of the algorithm. It divides
    !> the matrix into four submatrices:
    !>
    !>        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
    !>    A = [ -----|----- ]  with n1 = min(m,n)/2
    !>        [  A21 | A22  ]       n2 = n-n1
    !>
    !>                                       [ A11 ]
    !> The subroutine calls itself to factor [ --- ],
    !>                                       [ A12 ]
    !>                 [ A12 ]
    !> do the swaps on [ --- ], solve A12, update A22,
    !>                 [ A22 ]
    !>
    !> then calls itself to factor A22 and do the swaps on A21.
    !>
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix to be factored.
    !>          On exit, the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (min(M,N))
    !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
    !>          matrix was interchanged with row IPIV(i).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
    !>                has been completed, but the factor U is exactly
    !>                singular, and division by zero will occur if it is used
    !>                to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 112 of file zgetrf2.f.

Author

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